Complex-city

Algebra Level 4

Let the number of all complex numbers \(z_1\) which satisfy \(z_1^{3}-\bar{z_1}=0\) be \(a\).

If \(\arg\left(\dfrac{z_2-2}{z_2+2}\right)=\dfrac{\pi}{4}\), then locus of \(z_2\) is \(|z_2-bi|=\sqrt{c}\).

Find \(a+b+c\).

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